Nonmonotonic Lyapunov Function Control Based On Discrete T-S Fuzzy Systems

With the development of computer technology,the control requirements of complex nonlinear systems are increasing gradually.T-S fuzzy system is composed of a series of membership functions and linear subsystems.It can approximate nonlinear system with arbitrary precision.By means of T-S fuzzy system,a large number of traditional linear system control methods can be ef-fectively applied to the control of nonlinear system,which greatly simplifies the control design problem of nonlinear system.Aiming at the conservative problem in discrete T-S fuzzy control systems,this paper studies a robust con-trol method based on non-monotonic Lyapunov function to achieve better con-trol effect.The details are as follows:First of all,a non-parallel distributed compensation controller is designed for the discrete T-S fuzzy system with external disturbance.And then the ro-bustness analysis of the obtained closed-loop system is performed based on the fuzzy Lyapunov function:Firstly,the constraint matrices under different rules are constructed by Kronecker product algorithm to construct an augmented ma-trix,then the intermediate matrix is introduced to scale the constraint condi-tions,and then the robustness conditions of the system are obtained,and the H_∞robust stability conditions are transformed into linear matrix inequalities.On this basis,the non-monotone Lyapunov function method is introduced,and the non-monotone robust performance index is proposed to design the system,then the less conservative robust condition is obtained.Finally,a simulation example is given to compare the design methods based on monotonic and non-monotonic Lyapunov functions,so as to verify the effectiveness of the non-monotonic methods.Secondly,in order to further improve the system performance,a non-mon-otonic Lyapunov function method based on membership dependence is proposed.Firstly,the membership function is segmented in the H_∞robust per-formance analysis of the closed-loop system,and then the membership between the vertices of each segment is linearized.The upper and lower bounds of the difference between the original membership and the linearized membership are calculated and introduced into the robustness condition.What is more,the pro-posed non-monotone robust performance index analysis method is used to im-prove the design,then the obtained condition of robust stability of the closed-loop system is transformed into linear matrix inequalities.Finally,the simula-tion results show that the proposed control method can effectively improve the robustness and control performance of the system.